System and method for quantitative verification of flow measurements

ABSTRACT

A flow meter system and method measures fluid flow in a conduit. The conduit has a conduit axis. The flow meter includes a sensor configured to provide measurement data relating to the volumetric or mass flowrate though the conduit, and a processor configured to determine flow per unit time in the conduit using the measurement data, an uncertainty measurement per unit time using the measurement data, and an uncertainty quantity using the uncertainty measurement per unit time. The uncertainty quantity is totaled over a time period.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application claims the benefit of and priority to U.S. Application Ser. No. 63/114,407 filed Nov. 16, 2020, by Otto and Brown incorporated herein by reference in its entirety.

BACKGROUND OF THE INVENTION

The present disclosure is related to an electronic flow meter or electronic flow measurement device. Flow meters include, but are not limited to, ultrasonic flow meters, Coriolis flowmeters, electromagnetic flowmeters, thermal mass flow meters and differential pressure flow meters. U.S. Pat. Nos. 9,304,024, 10,288,462 and 10,393,568 and United States Patent Application Publication No. 2015/0198470 A1, entitled, “Self-Checking Flow Meter and Method” describe electronic flow meters and are incorporated herein by reference in their entireties. Electronic flow meters utilize measured sensor parameters to compute flow variables in real time. Some meters integrate the flow rate over a measurement cycle and aggregate the integrated value to provide a flow total in volumetric or mass terms.

Electronic flow measurement devices measure parameters and relate these to a measurand which can be, for example, flow velocity, volumetric flowrate or mass flowrate. In addition to interpretation of sensor data to infer the primary measurand, many electronic flow meters also have diagnostic functions. These diagnostic functions are usually qualitative in nature, i.e. they are expressed in terms that are different to the primary measurands. For example, an ultrasonic meter could provide measures of signal quality such as amplifier gain or signal-to-noise ratio. Although qualitative diagnostics are useful, it can be difficult for the user of a flow meter to interpret these diagnostics, as they do not relate directly to the measurand. In principle, it is possible for sensor diagnostics to be interpreted in terms of the measurand (for example by machine learning), or for additional sensors to be incorporated into a measurement device that will allow uncertainty in the primary measurand to be interpreted in quantitative terms, i.e. in the same units of measurement as the primary measurand

Some electronic flow meters determine flow based on the principles of ultrasonic transit time measurement. Transit time ultrasonic flow meters are capable of high accuracy performance over a wide range of application conditions. This has led to their adoption in applications such as custody transfer of hydrocarbons, and measurement of nuclear feedwater flows. To achieve high accuracy it is common for transit time ultrasonic flow meters to employ multiple pairs of transducers to infer velocity on a number of discrete paths. Chordal integration methods have been used in transit time ultrasonic flowmeters. By choosing the path locations and combining the individual velocity measurements according to rules for numerical integration, the result can represent the velocity integrated or averaged over the cross-section, and hence the volumetric flowrate, i.e.

$\overset{\_}{v} = {\sum\limits_{i = 1}^{N}{w_{i}{v\left( h_{i} \right)}}}$ $Q = {{\overset{\_}{v}A} = {A{\sum\limits_{i = 1}^{N}{w_{i}{v\left( h_{i} \right)}}}}}$

where Q is volumetric flowrate, v is average velocity, A is cross-sectional area, v(h_(i)) is the path velocity at distance h_(i), and w_(i), is the factor used to weight the velocity measurement before summation. Chord locations (h_(i)) and weighting factors (w_(i)) based on the rules of Gaussian integration are commonly chosen, based on either Legendre or Jacobi polynomials. Alternative integration schemes such as Chebyshev or Lobatto methods can also be applied. Other methodologies can also be applied to combining the velocity measurements along with information on geometry to produce a measure of volumetric flowrate. Two features of ultrasonic meters are particularly attractive in many applications. Firstly, they can be designed to be non-intrusive, that is to present little blockage to the flow, and consequently produce insignificant pressure loss. Secondly, their self-diagnostic capabilities and potential are attractive in applications where routine in-situ calibration is difficult for practical or cost reasons.

Currently the self-diagnostic capabilities of transit time ultrasonic meters are based on evaluation of parameters such as amplifier gain, signal-to-noise ratios, and velocity profile descriptors such as flatness, asymmetry and swirl. [Peterson, S, Lightbody, C, Trail, J and Coughlan, L (2008), On-line Condition Based Monitoring of Gas USM's, Proceedings of the North Sea Flow Measurement Workshop, Scotland, October 2008; Kneisley, G, Lansing, J, Dietz, T (2009) Ultrasonic Meter Condition Based Monitoring—a Fully Automated Solution, Proceedings of the North Sea Flow Measurement Workshop, Norway, October 2009]. However, as these parameters are difficult to relate directly to the uncertainty of the flow measurement, the use of qualitative meter diagnostics alone is not presently regarded as wholly sufficient as a means of flow meter verification. For example, in the 2003 edition of the Measurement Guidelines of the UK offshore oil and gas measurement regulator, while recognizing the benefits of current diagnostic techniques, note that they have the disadvantage that “diagnostic facilities are presently qualitative, rather than quantitative” [Department of Trade and Industry, Licensing and Consents Unit, Guidance Notes for Petroleum Measurement Under the Petroleum (Production) Regulations, December 2003, Issue 7]. In order to overcome this limitation, sometimes two flow meters are installed in series, i.e. with one a short distance downstream of the other. This allows the volumetric flowrates from the two flow meters to be compared with one another, with the result that the verification is quantitative, rather than qualitative. Taking this concept a step further, it has also been known to calculate two independent flow rate measurements using two independent subsets of transducers installed in a single meter body.

One example of such a meter design is the combination of a 4-path meter and a single path meter. [Kneisley, G, Lansing, J, Dietz, T (2009) Ultrasonic Meter Condition Based Monitoring—a Fully Automated Solution, Proceedings of the North Sea Flow Measurement Workshop, Norway, October 2009]. A disadvantage of this design is that the single path meter is much more sensitive to distortions of the flow velocity field than the 4-path meter. This difference in sensitivity means that when a difference is detected, there exists the possibility that the single path meter can be affected by a distortion of the flow field that has a negligible effect on the 4-path meter. In the case where the four-path meter is used as the primary measurement, this could result in false alarms, i.e. the difference detected does not reflect a reduction in accuracy of the 4-path meter. For example, in the referenced paper it is shown that when a flow conditioner upstream of the meter has one hole become blocked, there is virtually no effect on the 4-path meter, whereas the effect on the single-path meter can be greater than 0.85%. If, for example, an alarm threshold of 0.5% was set for the difference between the 4-path and single path result, the outcome would be an alarm annunciation where in fact the 4-path meter is continuing to read accurately.

Other examples of this concept include using two similar but separate groups of ultrasonic paths. An arrangement of eight paths can be used where one set of four paths are all set at a first angle relative to the pipe axis and the second set of four paths are all set at the negative value of that angle, such that the paths form a symmetrical X about the pipe axis when viewed from above. An alternative arrangement can be used whereby each independent set of four paths has paths selected alternately relative to the pipe axis. However, both of these arrangements suffer from a common weakness in that each group of four paths will still be affected differently by distortions of the flow velocity field, particularly when complex non-axial flow fields such as asymmetric rotational are present. What will happen in such a case is that one group of four paths will produce a result that will overestimate the flow rate, whilst the other group will underestimate the flow rate. Whilst this has some use in diagnosing flow conditions, it complicates the process of meter verification, as it is difficult to distinguish between an error in the measurement system itself and a difference that is created by the flow velocity field. There is a need for more precise or accurate determinations of diagnostic information for flow meters, such as uncertainty information.

The aforementioned patents and applications describe ultrasonic flow meter systems where additional measurements are incorporated to enable estimation of flow measurement uncertainty. Such a system can use various measurement parameters to infer various components of uncertainty in the flow measurement, including but not limited to uncertainty in the primary velocity measurements, in the integration of the axial velocity profile and in the cross-sectional area used to convert velocity to volumetric rate.

SUMMARY OF THE INVENTION

Some embodiments relate to a flow meter system for measuring fluid flow in a conduit. The conduit has a conduit axis. The flow meter includes a sensor configured to provide measurement data relating to the volumetric or mass flowrate though the conduit, and a processor configured to determine flow per unit time in the conduit using the measurement data, an uncertainty measurement per unit time using the measurement data, and an uncertainty quantity using the uncertainty measurement per unit time. The uncertainty quantity is totaled over a time period.

Some embodiments relate to a flow meter system for measuring fluid flow in a conduit having a conduit axis. The flow meter system includes a sensor configured to provide measurement data and a processor. The processor is configured to determine flow in quantity units per unit time in the conduit using the measurement data, at least one uncertainty value in quantity units per unit time using the measurement data, and at least one uncertainty quantity using the uncertainty value per unit time. The uncertainty quantity is totaled over a time period.

Some embodiments relate to an ultrasonic flow meter system for measuring fluid flow in a conduit having a conduit axis. The ultrasonic flow meter system includes multiple transducer pairs positioned to form acoustic transmission paths, some of which are co-located in one or more chordal measurement planes. In each chordal measurement plane, the multiple transducer pairs located in the chordal measurement plane are positioned to form acoustic transmission paths that traverse at least once from one side to the other and whereby axial velocity measurements are made in each chordal plane with a minimum of three traverses in each chordal plane. Each chordal plane is in parallel with the conduit axis. The ultrasonic flow meter system also includes a processor configured to determine flow per unit time in the conduit using the axial velocity measurements, an uncertainty measurement per unit time using the co-located chordal ultrasonic measurements and other inputs, and an uncertainty quantity using the uncertainty measurement per unit time. The uncertainty quantity is totaled over a time period.

Some embodiments relate to a method of measuring fluid flow in a conduit with a flow meter. The flow meter includes multiple transducer pairs positioned with respect to the conduit acoustic transmission paths, some of which are co-located in one or more chordal measurement planes. The method includes operations of: providing for each chordal measurement plane an axial velocity measurement, providing a flow per unit time in the conduit using the axial velocity measurement for each chordal plane, providing an uncertainty measurement per unit time for each chordal plane using the co-located measurements paths for each chordal plane, providing an uncertainty quantity for each chordal plane using the uncertainty measurement per unit time, and providing a total uncertainty quantity per chordal plane for a time period.

Some embodiments are directed toward a self-checking ultrasonic flow meter that provides an output of flow rate plus an associated estimate of uncertainty due to changes that could have affected the accuracy of the measurement system. The estimate of uncertainty is totalized as a quantity. In some embodiments, the estimate of uncertainty is not affected by asymmetric rotational flows, therefore eliminating the need for mechanical flow conditioning. This is achieved by arranging transducers such that redundant measurements of axial velocity can be made in each chordal measurement plane of the flow meter, i.e. multiple axial measurements are made in each chordal plane in such a way that they are substantially independent of the effects of non-axial or transverse flow. This dictates that there should be a minimum of six nodes in each chordal measurement plane, where each node is either a single transducer or a single reflection point. The compound axial velocity measurements in each measurement plane are then used in the computation of the flow rate, and comparison of individual in-plane axial velocity measurements used in the assessment of the uncertainty. Some embodiments are able to detect path angle and path length changes that would result from contamination build up inside the meter body, and to be able to do this for each chordal plane without reference to the data from another chordal plane. To that end, the velocity measurements within each chordal plane are made using pairs of transducers arranged such that one path has a path length divided by a cosine of the angle relative to the conduit axis that is different from another path in that same plane. Combining these constraints the flow meter would have transducers forming a minimum of three traverses in each chordal plane, at least one path having a path length or path angle that is different to the others in that plane. Other numbers of paths per chordal planes can be used and additional measurements and sensed values can be utilized in some embodiments.

In some embodiments, elements of uncertainty from other input measurements can be incorporated. For example, an ultrasonic measurement path that reflects off of the bottom of the pipe can be used to check if there is liquid present in the flow conduit of a ultrasonic gas meter, or a path that reflects off of the top of the pipe can be used to determine if there is gas present in the flow conduit of a ultrasonic liquid flow meter. Data from the reflective path can be used to evaluate uncertainty in the cross-sectional area of the conduit, which can then also be converted to an uncertainty in volumetric flow rate terms and be totalized along with the other components of uncertainty in some embodiments.

In some embodiments, in addition to the uncertainty owing to the measurement of axial velocity on each of the chordal measurement plains, uncertainty can arise as a result of how well the combination of the velocities measured on the discrete planes represents the velocity over the whole cross-section of the flow conduit. A separate patent U.S. Pat. No. 10,393,568 describes a method by which this component of uncertainty can be estimated by comparing the results of multiple integration methods. As such, this can be yet another component of uncertainty that is evaluated and totalized according to some embodiments.

Each individual component of uncertainty can be evaluated, converted to quantity units, and totalized individually. Furthermore, the various components can be combined to produce an overall uncertainty result in quantity units that can also be totalized. By totalizing both the contributing components of uncertainty and the overall uncertainty, the resulting uncertainty totals can be reviewed to determine which sources or components of uncertainty are making the most significant contributions to the overall uncertainty.

Although specific examples of how flow measurement uncertainty data can be obtained are described above, the systems and method described herein are not limited to such examples. Other flow measurement uncertainty data can be used. In some embodiments, an additional component of uncertainty owing to the detection of two-phase flow conditions (liquid-in-gas or gas-in-liquid) can be evaluated and totalized. In some embodiments an additional component of uncertainty owing to signal loss can be evaluated and totalized.

Other sensing modalities other than ultrasonic may also be used. For example, an estimate of uncertainty owing to analysis of multiple differential pressure signals, could be converted to flow units and totaled. Similarly, Coriolis sensor outputs could be combined with other measurements to evaluate uncertainties that could also be converted to flow units and totaled.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features, aspects, and advantages of the present invention will become apparent from the following description, appended claims, and the accompanying exemplary embodiments shown in the drawings, which are briefly described below:

FIG. 1 is a general block diagram of a flow measurement system including an uncertainty totalization module according to some embodiments.

FIG. 2 is a flow diagram showing uncertainty totalization operations for the system illustrated in FIG. 1 according to some embodiments.

FIG. 3 is a block diagram of a flow measurement system including a four chordal plane sensing system according to some embodiments.

FIG. 4 is a flow diagram showing uncertainty totalization operations for the system illustrated in FIG. 3 according to some embodiments.

FIG. 5 is a block diagram of a flow measurement system including a five chordal plane sensing system according to some embodiments.

FIG. 6 is a flow diagram showing uncertainty totalization operations for the system illustrated in FIG. 5 according to some embodiments.

DETAILED DESCRIPTION

Systems and methods according to certain embodiments utilize additional data to improve flow determinations. Users of flow measurement devices, particularly in areas where accuracy is critical such as liquid or gas custody transfer, have ever increasing expectations that the device should be able to provide not only the measurement result, but information that enables the user to evaluate the accuracy of the result. While flow measurement diagnostics are increasingly being monitored in real-time or even archived for later review, these diagnostics are qualitative in nature and are generally evaluated relative to experience-based limits or historical records of the same parameters, rather than being a quantitative evaluation of measurement uncertainty. The incorporation of quantitative self-diagnosis into flowmeters is described in U.S. Pat. Nos. 9,304,024, 10,288,462 and 10,393,568, incorporated herein by reference in their entireties, and requires processing, recording and presenting this information in a practical and meaningful way. In some embodiments, diagnostics values can be presented in real-time or can be recorded at intervals, preserving information about uncertainty in real-time. In some embodiments, post-processing this data presents a potentially large data storage and analytical burden. Conventional condition-based monitoring systems for ultrasonic meters, though sophisticated, lack a clear and practical way of providing the user with an evaluation of uncertainty over a given time period of interest.

Diagnostics in flow measurement devices can be both qualitative and transient in nature. For example, the amplification (gain) applied to a pair of ultrasonic transducers in an ultrasonic flow meter may be determined and can be monitored relative to an alarm limit or recorded at intervals in a database. In the event of a problem occurring, it is therefore possible to examine the diagnostic data and infer some information about what the problem may be and when it occurred. The question that the user will often then have is: what was the impact of this event on my measurement results? However, the information available from such qualitative diagnostics are not and generally cannot be expressed in the same quantitative terms as the flow measurement itself, and therefore the knowledge conveyed by this form of diagnostic is unsatisfactory in terms of understanding how the problems have contributed to uncertainty in the measurement result.

In some embodiments, systems and methods provide an electronic flow meter with self-verification, whereby various elements of uncertainty are continually evaluated, combined and totalized in the same terms as the totalization of the primary flow measurement, i.e. mass or volume. In some embodiments, systems and methods evaluate additional data to derive components of measurement uncertainty terms in units of volumetric or mass flow, and each of these components is integrated and totalized. In some embodiments, the accumulated or totalized flow (in volume or mass terms) is presented with a corresponding uncertainty in that total. In addition to the overall totalized uncertainty, totalization can be provided for individual components of uncertainty, providing insight into how individual components of uncertainty have contributed to the overall uncertainty in the reported total.

In some embodiments, the measurement technology is based on the measurement of the transit time of ultrasonic pulses and the uncertainty contributions are determined from a number of sources, including but not limited to:

-   -   Signal-to-noise ratio of signals.     -   Difference between computed axial velocities on each chordal         plane (see e.g., U.S. Pat. No. 9,304,024).     -   Difference between dissimilar chordal integration methods (see         e.g., U.S. Pat. No. 10,393,568).     -   Estimation of area blockage using ultrasonic ranging techniques         to determine the uncertainty in the cross-sectional area used in         the conversion of velocity to volumetric rate.

Other measurement technologies can also be employed to estimate individual components of uncertainty. For example, a measurement system using a variety of different sensing principles could be used to generate estimates of uncertainty. For example, a two-component oil and water flow meter could use an ultrasonic meter, a differential pressure measurement and a capacitance meter to estimate the total flowrate of both the water and oil in a flowing two-component mixture. The volumetric rate derived from the differential pressure measurement could be compared with the volumetric rate derived from the ultrasonic measurements, providing inputs for estimation of one component of uncertainty (the uncertainty in the total volumetric flowrate). The oil/water fraction could be estimated from both the measured speed of sound from the ultrasonic meter and from the capacitance measurements, and these two sets of measurements could be used to estimate another component of uncertainty (the uncertainty in the oil/water fraction). For the water flowrate and the oil flowrate, the uncertainties for each of the components (i.e. volumetric rate and oil/water fraction) can be expressed as quantities and totaled, and they can also be combined to estimate the overall uncertainty in the oil and water quantities, with the overall results also being totaled.

In some embodiments, systems and methods of flow measurement describe herein are able to calculate, preserve and communicate information related to measured parameters as a continuous totalization of measurement uncertainty in terms of mass or volume. Uncertainties are estimated in terms of absolute values, which can then be converted into the same quantitative terms as the primary quantity or quantities measured by the flow meter, and these can then be totalized individually. As well as being provided for totalization, the component uncertainties are also combined according to the principles of uncertainty estimation, and a totalisation of the overall uncertainty is performed. The result is that totalized values can be preserved for both the primary quantity (or quantities if a meter is able, for example, to compute both mass and volume, or to compute quantities of individual constituents of a flow such as oil and water) and for the individual components of uncertainty.

In some embodiments, a flow meter sensor, such as an ultrasonic meter, is configured to evaluate additional data to derive various components of measurement uncertainty. The flow meter provides the measurement uncertainties in units of volumetric or mass flow, and each of these components is integrated and totalized. Although particular types and technologies of flow metering are described below, the systems and methods can be utilized with other types of meters or sensors in various applications in some embodiments.

A self-verifying ultrasonic meter using the principles outlined in U.S. Pat. Nos. 9,304,024, 10,288,462, and 10,393,568 utilizes an electronic signal processing unit and a number of transducers to make multiple measurements of the transit time of ultrasonic pulses sent along specific paths in a flowing fluid. These paths are arranged to allow the meter to make a plurality of axial velocity measurements in each chordal plane of a multipath ultrasonic flow meter in some embodiments. The resulting measurements can be utilized to determine the rate and quantity of flow and also to estimate the uncertainty in that flowrate in some embodiments. For each chordal plane, the difference between the axial velocity results is used to determine an uncertainty component in terms of velocity (e.g. meters per second) for that chordal plane in some embodiments. That component uncertainty for the given chordal plane can then be converted to an uncertainty in volumetric flowrate by using appropriate weighting and geometric terms in some embodiments. Multiplying the component measure of volumetric flowrate uncertainty with its corresponding time interval, an integrated result in terms of volume uncertainty is produced in some embodiments. At each calculation cycle, the volume uncertainty increment is added to the previous value for that given component of uncertainty, resulting in an uncertainty volume totalization in some embodiments. During each calculation cycle, an overall uncertainty is also calculated by combining the various component uncertainty inputs in some embodiments.

With reference to FIG. 1, a system 1 includes a processor 2, a vessel, conduit, or pipe 3 through which a fluid or fluid/solid mixture (e.g., a gas, liquid, fluids with sediments, or mixtures thereof) is provided at a flow rate, and a sensor 4 configured to provide data for determining a flow rate. Sensor 4 is a unit that is an assembly of sensor technologies that respond to flow and related measurands in some embodiments. Sensor 4 can be an ultrasonic sensor including multiple transducers as described below and in U.S. Pat. Nos. 9,304,024, 10,288,462, and 10,393,568. The sensor 4 provides signals which are converted to flow data and additional data in the processor 2. Sensor 4 can be coupled to the processor 2 wirelessly (dashed line) or via a wired connection.

The processor 2 is configured to determine the flow in terms of flow rate and total mass and/or volume provided over time through the pipe 3 and uncertainty based upon the flow data and the additional data. The flow rate, total mass or volume and uncertainty can be provided on a display 5 or communicated digitally to another system (e.g., via analog or digital inputs and outputs 13). The additional data can be utilized to evaluate various sources of uncertainty in the form of individual component uncertainties, and could include signal-to-noise ratio measurements and additional transit time measurements to allow for evaluation of velocity uncertainty, additional velocity measurements to allow for evaluation of flow profile uncertainty, and ultrasonic evaluation of the cross-sectional area of the pipe.

Other and various measurements can be included and translated into a component uncertainty in units of volumetric or mass rate in some embodiments. Measurement data can be provided via analog or digital inputs and outputs 13. For example, two measurements could be used to infer two values of density, and hence a component uncertainty in units of density that can then be converted to uncertainty in mass flow terms by multiplication with the volumetric flowrate. The component uncertainty for density can then be totaled on a mass basis. Some available diagnostics are not readily amenable to this treatment. For example, in general use the amplifier gain cannot be directly related to an uncertainty in flow rate terms and could only be used in this way if a relationship between gain and flowrate uncertainty was established empirically for very specific set of circumstances.

The processor 2 can be any hardware and/or software processor or processing architecture configured to execute instructions and operate on data from the sensor 4 and other sources. The processor 2 can be include a wired or wireless interface for communicating with the sensor 4. The processor 2 can be or can include one or more microprocessors, application specific integrated circuits (ASICs), circuits containing one or more processing components, groups of distributed processing components, circuits for supporting a microprocessor, or hardware devices configured for processing sensor data. In some embodiments, the processor 2 and the display 5 are part of a computer, server, a mobile computing device, or work station and are separate from the sensor 4. In some embodiments, the processor 2 can be integrated or mounted with the sensor 4 or the pipe 3, a network associated with the sensor 4, or a remote data center. In some embodiments, the display 5 is a liquid crystal display in the flow meter or sensor 4 that provides the totalized uncertainty value. In some embodiments, the display 5 is on a smart phone or other hand held device or is integrated with the sensor 4.

In some embodiments, the processor 2 includes a non-transitory medium, such as a memory, for storing software instructions for making flow determinations and uncertainty determinations. In some embodiments, the processor 2 includes a flow calculation module 6, an uncertainty calculation module 7, a flow totalization module 8, an uncertainty calculation module 9, an uncertainty totalization module 11, and a signal processing module 15. Modules 6, 8, 9, 11, and 15 can be implemented in hardware or software or combinations thereof and can be integrated together. In some embodiments, one or more of modules 6, 8, 9, 11, and 15 is provided with the sensor 4 or shared between the processor 2 and the sensor 4.

In some embodiments, the sensor 4 is configured as a multipath ultrasonic flow meter to make a number of transit time measurements for determination of multiple axial velocities (e.g., 2 or more) in each chordal plane. The transit time measurements are provided to the flow calculation module 6 and flow totalization module 8 of the processor 2 to determine the rate and quantity of flow. In some embodiments, the signal processing module 15 converts the signal from the sensor 4 into digital information and is in communication with the processor 2 to both send and receive data and/or commands. The uncertainty calculation module 9 also receives the transit time measurements as well as additional data to determine the uncertainty in that flow rate in some embodiments. For each chordal plane, the difference between the axial velocity results is used to determine an uncertainty component in terms of velocity (e.g. meters per second) for that chordal plane in some embodiments. The component uncertainty for the given chordal plane can then be converted to an uncertainty in volumetric flowrate by using appropriate weighting and geometric terms in some embodiments. Multiplying the component measure of volumetric flowrate with its corresponding time interval, an integrated result in terms of volume is produced in some embodiments. In some embodiments, the uncertainty totalization module 11 adds the volume increment at each calculation cycle to the previous value for that given component of uncertainty, resulting in an uncertainty volume totalization in some embodiments. During each calculation cycle, an overall uncertainty is calculated by combining the various component uncertainty inputs and is totalized in some embodiments.

In some embodiments, axial velocities are determined in five chordal measurement planes. Two subsets of these axial velocities can be utilized to make two estimates of the average velocity over the cross-section of the flow conduit, for example using the data from four chordal planes in one case and from all five chordal planes in another. This is achieved by using two different sets of weighting factors, one for the four-chord result and another set of weighing factors for the five-chord result. Comparing cross-sectional average velocity measurements from the four-chord and five-chord results can be used to determine a component of uncertainty related to the flow velocity profile. A larger difference in average velocities calculated from the two different velocity measurements results in a larger value for this component of uncertainty. In some embodiments, an additional measurement path (e.g., from top to bottom) is used to estimate another component of uncertainty that is related to the value of the cross-sectional area that is used in the flow measurement calculations. In other words, an uncertainty component for area is estimated using this path. That component of uncertainty is converted to an uncertainty in volumetric rate by multiplication with the average velocity over the cross-section, and can then be integrated and totaled as a volume.

Examples 1, 2 and 3 are worked examples in tabular form and are shown below. These illustrate a case where three components of uncertainty have been estimated based on the measurements and additional data available to the flow meter. These component uncertainties could be one of the component uncertainties already described or some other component uncertainty. As well as the individual component uncertainties, an overall uncertainty is determined by combining the individual component uncertainties. In Examples 1, 2, and 3, the primary flowrate is held constant, and the component uncertainties vary between one and the other of two values to make it easier to illustrate the principles at work, and should not be considered as a limiting case. In a real case, flowrates and uncertainties can be varying continuously, as will be familiar to practitioners in the fields of flow metering and measurement uncertainty.

Columns 1 and 2 of each of the Examples 1-3 show the elapsed time and the time interval between successive measurements/calculations. The processor 2 provides the data for Examples 1, 2 and 3 in response to sensor measurements from sensor 4 in some embodiments. The primary flowrate measurement and the corresponding totalized volume are shown in columns 3 and 4. The columns 5, 6, and 7 that follow show uncertainty values in cubic meters per hour for three different components that contribute to the overall uncertainty. Each of the three components could be associated with one of three chordal planes in some embodiments. In another embodiment the three components could be uncertainties associated with axial velocity measurement, the influence of velocity profile, and the uncertainty in cross-section area respectively. Different, and additional components can be utilized with no limit on the total number of components, with the examples using only three components to simplify the description.

Columns 8, 9, and 10 show the process of totalizing the uncertainty components, and columns 11 and 12 show the overall uncertainty and its totalization. The values in cubic meters shown in columns 8, 9, 10, and 12 are the totalization results which can be stored as single values (i.e. only the latest value available) or written at intervals to an internal memory in a flow measurement device, such as system 1.

These totalized values advantageously retain the essential information about the uncertainty of the measurement during the whole interval between the recorded results while either available only as single results at the end of a process or with relatively long intervals between records (minutes, days, months, etc.). Although only 10 seconds is shown in Examples 1, 2, and 3, in practice totalization can continue for much longer durations (e.g., hours, days, weeks, etc.). Examples 1, 2, and 3 illustrate relevant uncertainty information related to the throughput that can be very quickly and easily evaluated by reviewing the totalized values covering at the end of a period of interest. Example 1 alone illustrates that by totalizing the individual component uncertainties as well as the overall uncertainty, the component of uncertainty that is largest can be determined and potentially gives insights as the to the underlying cause of the uncertainty and ways in which uncertainty might be reduced.

In some embodiments, the totalized uncertainty values are compared corresponding thresholds by the totalization module 11. When the uncertainty for a given component or for the overall uncertainty exceeds the threshold associated with that component, an alarm can be provided on display 5 by the processor 2 or can be transmitted digital or by means of an output such as an electronic switch controlling a DC voltage.

Another advantageous feature of system 1 can be illustrated by comparing the root-sum-square combination of the individual component uncertainties (totalized at the end of the 10-second time period or any actual time period in question) with the overall totalized uncertainty that has been totalized continually during the same period according to some embodiments. By comparing Examples 2 and 3, it can be observed that at the end of the 10 seconds the overall total uncertainty is not the same in Examples 2 and 3 and yet the totalized uncertainty for each individual component is the same in those examples (compare columns 11-12 and columns 8-10 in Examples 2 and 3). This illustrates the advantage and utility of calculating and recording both the individual and overall uncertainty totals, as recording only the component totals and combining those at the end of the time period would yield a different (and essentially incorrect) result relative to the continuous totalization of the overall uncertainty. The underlying cause is that the component uncertainties highlighted by underlining in Examples 2 and 3 increase to 20 m³/hr concurrently in Example 2, and increase to 20 m³/hr at separate times in Example 3. This shows that the process of totalizing the component and overall uncertainties accounts for and preserves certain information that would otherwise be lost at the end of the ten second interval. Examples 1-3 illustrate the advantages of calculating and totalising the overall uncertainty at each interval. If the detail of what happens at each interval not retained, then it is not possible retrospectively to account for how the various components of uncertainty combine at a particular point in time. It is the totalisation process that enables that information to be preserved without burdening the system with a large data retention requirement.

8 9 10 12 13 5 6 7 Total- Total- Total- Overall Overall 2 4 Uncer- Uncer- Uncer- ised ised ised 11 Total- Total- 1 Time 3 Total- tainty tainty tainty Uncer- Uncer- Uncer- Overall ised ised Elapsed inter- Flow ised compo- compo- compo- tainty for tainty for tainty for Uncer- Uncer- Uncer- time val rate volume nent 1 nent 2 nent 3 comp. 1 comp. 2 comp. 3 tainty tainty tainty s s m3/hr m3 m3/hr m3/hr m3/hr m3 m3 m3 m3/hr m3 % 1 1 3600.0 1.0 3.60 4.50 1.80 0.0010 0.0013 0.0005 6.04 0.001677 0.168% 2 1 3600.0 2.0 3.60 4.50 1.80 0.0020 0.0025 0.0010 6.04 0.003354 0.168% 3 1 3600.0 3.0 3.60 4.50 1.80 0.0030 0.0038 0.0015 6.04 0.005031 0.168% 4 1 3600.0 4.0 3.60 4.50 1.80 0.0040 0.0050 0.0020 6.04 0.006708 0.168% 5 1 3600.0 5.0 3.60 4.50 1.80 0.0050 0.0063 0.0025 6.04 0.008385 0.168% 6 1 3600.0 6.0 3.60 4.50 1.80 0.0060 0.0075 0.0030 6.04 0.010062 0.168% 7 1 3600.0 7.0 3.60 4.50 1.80 0.0070 0.0088 0.0035 6.04 0.011739 0.168% 8 1 3600.0 8.0 3.60 4.50 1.80 0.0080 0.0100 0.0040 6.04 0.013416 0.168% 9 1 3600.0 9.0 3.60 4.50 1.80 0.0090 0.0113 0.0045 6.04 0.015093 0.168% 10 1 3600.0 10.0 3.60 4.50 1.80 0.0100 0.0125 0.0050 6.04 0.016771 0.16771% After-the-fact combination of Difference relative to overall component uncertainties totalised uncertainty 0.016771 m3 0.16771% 0.000000 m3 0.00000%

Example 1

8 9 10 12 13 5 6 7 Total- Total- Total- Overall Overall 2 4 Uncer- Uncer- Uncer- ised ised ised 11 Total- Total- 1 Time 3 Total- tainty tainty tainty Uncer- Uncer- Uncer- Overall ised ised Elapsed inter- Flow ised compo- compo- compo- tainty for tainty for tainty for Uncer- Uncer- Uncer- time val rate volume nent 1 nent 2 nent 3 comp. 1 comp. 2 comp. 3 tainty tainty tainty s s m3/hr m3 m3/hr m3/hr m3/hr m3 m3 m3 m3/hr m3 % 1 1 3600.0 1.0 3.60 4.50 1.80 0.0010 0.0013 0.0005 6.04 0.001677 0.168% 2 1 3600.0 2.0 3.60 4.50 1.80 0.0020 0.0025 0.0010 6.04 0.003354 0.168% 3 1 3600.0 3.0 3.60 4.50 1.80 0.0030 0.0038 0.0015 6.04 0.005031 0.168% 4 1 3600.0 4.0 3.60 4.50 1.80 0.0040 0.0050 0.0020 6.04 0.006708 0.168% 5 1 3600.0 5.0 3.60 4.50 1.80 0.0050 0.0063 0.0025 6.04 0.008385 0.168% 6 1 3600.0 6.0 3.60 4.50 1.80 0.0060 0.0075 0.0030 6.04 0.010062 0.168% 7 1 3600.0 7.0 3.60 4.50 1.80 0.0070 0.0088 0.0035 6.04 0.011739 0.168% 8 1 3600.0 8.0 20.00  20.00  20.00  0.0126 0.0143 0.0091 34.64 0.021362 0.267% 9 1 3600.0 9.0 20.00  20.00  20.00  0.0181 0.0199 0.0146 34.64 0.030984 0.344% 10 1 3600.0 10.0 20.00  20.00  20.00  0.0237 0.0254 0.0202 34.64 0.040607 0.40607% After-the-fact combination of Difference relative to overall component uncertainties totalised uncertainty 0.040160 m3 0.40160% 0.000447 m3 0.00447%

Example 2

8 9 10 12 13 5 6 7 Total- Total- Total- Overall Overall 2 4 Uncer- Uncer- Uncer- ised ised ised 11 Total- Total- 1 Time 3 Total- tainty tainty tainty Uncer- Uncer- Uncer- Overall ised ised Elapsed inter- Flow ised compo- compo- compo- tainty for tainty for tainty for Uncer- Uncer- Uncer- time val rate volume nent 1 nent 2 nent 3 comp. 1 comp. 2 comp. 3 tainty tainty tainty s s m3/hr m3 m3/hr m3/hr m3/hr m3 m3 m3 m3/hr m3 % 1 1 3600.0 1.0 3.60 4.50 1.80 0.0010 0.0013 0.0005 6.04 0.001677 0.168% 2 1 3600.0 2.0 20.00  4.50 1.80 0.0066 0.0025 0.0010 20.58 0.007393 0.370% 3 1 3600.0 3.0 20.00  4.50 1.80 0.0121 0.0038 0.0015 20.58 0.013110 0.437% 4 1 3600.0 4.0 20.00  4.50 1.80 0.0177 0.0050 0.0020 20.58 0.018826 0.471% 5 1 3600.0 5.0 3.60 20.00  1.80 0.0187 0.0106 0.0025 20.40 0.024493 0.490% 6 1 3600.0 6.0 3.60 20.00  1.80 0.0197 0.0161 0.0030 20.40 0.030160 0.503% 7 1 3600.0 7.0 3.60 20.00  1.80 0.0207 0.0217 0.0035 20.40 0.035827 0.512% 8 1 3600.0 8.0 3.60 4.50 20.00  0.0217 0.0229 0.0091 20.81 0.041609 0.520% 9 1 3600.0 9.0 3.60 4.50 20.00  0.0227 0.0242 0.0146 20.81 0.047390 0.527% 10 1 3600.0 10.0 3.60 4.50 20.00  0.0237 0.0254 0.0202 20.81 0.053172 0.53172% After-the-fact combination of Difference relative to overall component uncertainties totalised uncertainty 0.040160 m3 0.40160% 0.013012 m3 0.13012%

Example 3

Uncertainty values are combined according to various mathematical operations according to known practices in uncertainty evaluation. In some cases, the uncertainties describe a range within which that value is expected to fall, and when combined, all contributions are not expected to be at the extreme limits of their uncertainties at the same time. For example, the uncertainty values can be combined in a method that can (in simplified terms) be described as taking the square-root of the sum of the squared uncertainties. With such an approach, the component values do not simply add together to give the overall uncertainty. In other cases, uncertainty components may be added to one another linearly. Various mathematical techniques can be utilized to combine the totalized uncertainty values according to known conventions

With reference to FIG. 2, the flow diagram 200 can be used to explain the calculation process. The flow diagram 200 provides a basic uncertainty totalization process in some embodiments. The calculations described in the flow diagram 200 can be adjusted include various statistical or mathematical operations. At an operation 202, the calculation process begins. In an operation 204, the sensor 4 provides measurement steps to provide measurement data (e.g. sending and receiving ultrasonic pulses, measuring transit time, providing velocity data, providing communication data, etc.). The measurement data from the sensor 4 can be recorded in memory and stamped with time of sample, and other ancillary data for data processing operations. In an operation 204, primary flow computations are performed. The flow computations can be performed as described in U.S. Pat. Nos. 9,304,024, 10,288,462, and 10,393,568 by flow module 6 and flow totalization module 8, and examples of such measurements are described below in some embodiments. The flow measurements can be computed at a regular or irregular intervals, normally but not necessarily at a relatively fast rate such as once every second. In some embodiments the flow measurements can be based upon velocities inferred from measurements of ultrasonic transit times.

In an operation 208, the uncertainty calculation module 9 determines flow measurement uncertainty components in quantity units per unit of time (e.g., m³/s or kg/s) in some embodiments. Uncertainty components can be determined by various means including but not limited to comparing results different from different combinations of measurement data, evaluating signal-to-noise ratios or other diagnostic parameters or evaluating statistical values derived from the measurement data. Uncertainty components can be calculated by the processor 2 using uncertainty calculation module 9 according to the techniques described in U.S. Pat. Nos. 10,393,568 and 9,304,024 in some embodiments.

In an operation 210, the processor 2 determines the time interval between current and previous measurements (e.g., using time stamps). In an operation, 212, the processor 2 multiplies the uncertainty values by the time intervals to determine a quantity of uncertainty (e.g., in mass and/or volume). In an operation 214, the totalization module 8 adds respective uncertainty quantity values (in quantity units) to previous values to provide totalized uncertainty results (in quantity units). At operation 216, the process 200 returns to the operation 204 if more data is available or exits to a stop operation 218. The totalized uncertainty results can be recorded, stored or output on a periodic basis—once per day, once per hour, once per minute, etc. or can be recorded, stored or output for specific operations such as transfer of individual batches of fluid, e.g., in tanker loading operations.

In some embodiments, the uncertainty totalization can be used to validate the flow meter or determine when the flow meter requires investigation or repair. For example, when the uncertainty totalization in a given period reaches a predetermined threshold, the meter or sensor 4 can be flagged for further investigation, maintenance or replacement. The processor 2 can send a message or provide an indicator of an alarm and/or the quantity of totalized uncertainty. In some embodiments, the totalization can be divided by the time interval over which the total was accumulated and expressed in term of a flow rate. In some embodiments, the rate of change in the uncertainty totalization can be used to diagnose a problem in the sensor 4 or pipe 3. In some embodiments, the totalization of uncertainty can divided by the totalization of flow to determine an uncertainty in relative terms, e.g. as a ratio or percentage. Relative uncertainties may be used to indicate when investigation, maintenance, repair or replacement is required. For example, a relative uncertainty of 1 percent or less per total flow may indicate that the system 1 is measuring flow properly, while a higher percentage could indicate that remedial action is required.

With reference to FIG. 3, a system 25 is similar to systems 1 (FIG. 1) and includes processor 2, a vessel, conduit, or pipe 3 through which a fluid (e.g., a gas, liquid, fluids with sediments, or mixtures thereof) is provided at a flowrate, and a sensor 17 configured as an ultrasonic measurement sensor. Sensor 17 includes multiple transducers forming nodes and paths 21A-D, 22A-D, and 23A-D in four chordal planes 20A-20D. In the example shown in FIG. 3, sensor 17 has six nodes and three paths in each of chordal planes 20A-D in some embodiments.

With reference to FIG. 4, system 25 (FIG. 3) can use a flow and uncertainty calculation process 51 based on an sensor 17 with a number of axial velocity measurements 52A-D being performed in each of chordal planes 20A-D. Measurements 52A-D are measurement data from sensor 17. Measurement values/results 54A-D represent axial velocity results and measurement values/results 56A-D represent uncertainty values calculated from the measurement data. From the axial velocity results in each of the chordal planes 20A-D, an axial velocity value for that plane (e.g., results 54A-D) is calculated and an uncertainty in that axial velocity result is calculated (e.g., results 56A-D). The axial velocity results (e.g., results 54A-D) are combined to compute the flow measurement result, which is a volumetric flowrate 98. The volumetric flowrate 98 is provided to the flow totalization module 8 to obtain a volume total result. The uncertainty result 56A-D for each chordal plane 20A-D can be converted from units of velocity to units of volumetric flow rate. Each of the axial velocity uncertainties per chordal plane 20A-D, once expressed in terms of volumetric flowrate, can then be input to the uncertainty totalization module 9, and totalized in units of cubic meters. The individual axial velocity uncertainty results (e.g., results 56A-D) per chordal plane 20A-D are also combined to determine an overall uncertainty that represents the uncertainty in the measurement result owing to the combined effects of the uncertainty on each chord, shown as U Chordal result 88. U Chordal result 88 is also computed in volumetric flow rate terms and is an additional input to the uncertainty totalization calculated by uncertainty totalization module 11 (FIG. 3). An exemplary end result is a total volume measured by the meter 17 (i.e. the measurement result), and five uncertainty results, one for each of the chordal measurement planes 20A-D, and one for the combined measurement result (i.e., U Chordal 88). Examination of these totals allows for easy determination of the uncertainty over an extended period of time, including information on the respective contribution of the four measurement chords 20A-D to the overall measurement uncertainty.

With reference to FIG. 5, a system 81 is similar to systems 1 and 25 (FIGS. 1 and 3) and includes processor 2, a vessel, conduit, or pipe 3 through which a fluid (e.g., a gas, liquid, fluids with sediments, or mixtures thereof) is provided at a flow rate, and a sensor 85 configured as an ultrasonic measurement sensor. Sensor 85 can be similar to sensor 4 (FIG. 1) and includes multiple transducers forming nodes and paths 21A-E, 22A-E, and 23A-E in five chordal planes 20A-20E. In the example shown in FIG. 5, sensor 85 has six nodes and three paths in each of chordal planes 20A-E and two nodes associated with a V-path 83 extending through planes 20A-E in some embodiments.

With reference to FIG. 6, system 81 (FIG. 5) can use a flow and uncertainty calculation process 81 based on an sensor 85 with a number of axial velocity measurements 52A-E being performed in each of chordal planes 20A-E. Process 91 is similar to process 51 (FIG. 4) and uses additional measurements dedicated to determining additional components of uncertainty in some embodiments. Measurement values/results 54A-E are measurement data from sensor 85. Measurement values/results 54A-E represent axial velocity results and measurement values/results 56A-E represent uncertainty values calculated from the measurement data. From the axial velocity results in each of the chordal planes 20A-D, an axial velocity value for that plane (e.g., results 54A-D) is calculated and an uncertainty in that axial velocity result is calculated (e.g., results 56A-D). The axial velocity results (e.g., results 54A-D) are combined to compute the flow measurement result, velfourchord value 81, which is used to provide volumetric flowrate 98. The axial velocity value for plane 20E (e.g., result 52E) is used to calculate velfivechord value 78. The velfivechord value 78 enables calculation of an additional uncertainty component according to the techniques of U.S. Pat. No. 10,393,568 in some embodiments.

The four-chord combined velocity or velfourchord value 81 and the five-chord combined velocity or velfivechord value 78 are used compute an additional uncertainty component or U integration value 80. The U integration value 80 estimates uncertainty owing to the integration or averaging of the flow velocity profile. Furthermore, additional sensors and measurement results (e.g., sensors for area blockage estimation 94) are used in the calculation of another component of uncertainty, the uncertainty in the cross-sectional area or U Area value 84. Such results can be derived from data from additional measurements such as from measurements from V path 83 (FIG. 5). In process 91, the overall uncertainty or U Combined value 96 is computed using the uncertainty calculation module 72 (FIG. 5) from the three major components of uncertainty, the U Area value 84, the U Chordal value 88 and U Integration value 80. Therefore, in this example the process 91 includes the flow rate measurement result or flow rate value 98 and nine different uncertainties: the five uncertainty values for axial velocity (one per chordal measurement plane, e.g., results 56A-E), the three major components of the overall uncertainty (e.g., values 80, 84, and 88), and the overall uncertainty (e.g., value 96). When these nine uncertainty values and the flow rate value 98 are determined over an extended period of time, the examination of the totals allows for easy understanding of the overall uncertainty and the factors that have contributed that overall uncertainty. For example, the area uncertainty total or U area value 84 could be much larger than the combined chordal velocity total (e.g., value 82) or the integration uncertainty total (e.g., value 90), suggesting a process contamination problem. In a different example, the combined chordal velocity uncertainty (e.g., value 88) could have the largest uncertainty total and the uncertainty in the axial velocity on chordal plane 20B (value 56B) could be much larger than the totals for the other chords, indicating that there is a problem with the measurements on chordal plane 20B.

The volumetric flowrate 98 is input to the flow totalization module 8 to produce a volume total result. The uncertainty result 56A-D for each chordal plane 20A-D and result 56E for plane 20E can be converted from units of velocity to units of volumetric flow rate. Each of the axial velocity uncertainties per chordal plane 20A-E, once expressed in terms of volumetric flowrate, can then be input to the uncertainty totalization module 9, and totalized in units of cubic meters. The individual axial velocity uncertainty results (e.g., results 56A-D) per chordal plane 20A-D are also combined to determine an overall uncertainty that represents the uncertainty in the measurement result owing to the combined effects of the uncertainty on each chord, shown as U Chordal result 88. U Chordal result 88 is also computed in volumetric flow rate terms and is an additional input to the uncertainty totalization calculated by uncertainty totalization module 72 (FIG. 5).

While the detailed drawings, specific examples, and particular configurations given describe preferred and exemplary embodiments, they serve the purpose of illustration only. The inventions disclosed are not limited to the specific forms shown. For example, the methods may be performed in any of a variety of sequence of steps or according to any of a variety of mathematical formulas. The hardware and software configurations shown and described may differ depending on the chosen performance characteristics and physical characteristics of the communications devices. For example, the type of system components and their interconnections may differ. The systems and methods depicted and described are not limited to the precise details and conditions disclosed. The figures show preferred exemplary operations only. The specific data types and operations are shown in a non-limiting fashion. Furthermore, other substitutions, modifications, changes, and omissions may be made in the design, operating conditions, and arrangement of the exemplary embodiments without departing from the scope of the invention as expressed in the appended claims. 

What is claimed is:
 1. A flow meter system for measuring fluid flow in a conduit having a conduit axis, the flow meter system comprising: a sensor configured to provide measurement data; a processor configured to determine: flow in quantity units per unit time in the conduit using the measurement data at least one uncertainty value in quantity units per unit time using the measurement data, at least one uncertainty quantity using the uncertainty value per unit time, wherein the uncertainty quantity is totaled over a time period.
 2. The flow meter system of claim 1 wherein quantity units are in mass or volume.
 3. The flow meter system of claim 1 wherein the sensor comprises ultrasonic transducers in one or more chordal measurement planes, wherein transducer pairs located in each chordal measurement plane are positioned to form acoustic transmission paths that traverse at least once from one side of the chordal measurement plane to another side of the chordal measurement plane, each traverse is either direct from one transducer to another or via one or more reflection points and whereby a plurality of axial velocity measurements are made in each chordal plane with a minimum of three traverses in each chordal plane, each chordal plane is in parallel with the conduit axis.
 4. The flow meter system of claim 1, wherein the one uncertainty value in quantity units per unit time comprises a number of first measurements each associated with a unique chordal plane.
 5. The flow meter system of claim 4, wherein each of the first measurements are converted to respective first quantities.
 6. The flow meter system of claim 5, wherein the first quantities are totalized.
 7. An ultrasonic flow meter system for measuring fluid flow in a conduit having a conduit axis, the ultrasonic flow meter system comprising: multiple transducer pairs positioned to form acoustic transmission paths that are co-located in one or more chordal measurement planes in each chordal measurement plane; and a processor configured to determine flow per unit time in the conduit using the axial velocity measurements, an uncertainty measurement per unit time using the axial velocity measurements, and an uncertainty quantity using the uncertainty measurement per unit time, wherein the uncertainty quantity is totaled over a time period.
 8. The ultrasonic flow meter system of claim 7, wherein the uncertainty measurement is related to differences in the axial velocity measurements in each chordal plane.
 9. The ultrasonic flow meter system of claim 7, wherein the multiple transducer pairs located in the chordal measurement plane are positioned to form acoustic transmission paths that traverse at least once from one side and whereby a plurality of axial velocity measurements is made in each chordal plane with a minimum of three traverses in each chordal plane, each chordal plane is in parallel with the conduit axis, and comprising two paths per chordal plane, each path being a reflected path with two traverses of the chordal plane and one reflection in each of the two paths.
 10. The ultrasonic flow meter system of claim 9, comprising three paths per chordal plane and transmission on two paths is direct between transducers, and one path is a reflected path with two traverses of the chordal plane and one reflection point.
 11. The ultrasonic flow meter system of claim 7, wherein the uncertainty measurement per unit time comprises a number of first measurements each associated with a unique chordal plane.
 12. The ultrasonic flow meter system of claim 11, wherein each of the first measurements are converted to respective first quantities.
 13. The ultrasonic flow meter system of claim 12, wherein the first quantities are totalized.
 14. The ultrasonic flow meter system of claim 7, wherein the multiple transducer pairs located in the chordal measurement plane are positioned to form acoustic transmission paths that traverse at least once from one side and whereby a plurality of axial velocity measurements is made in each chordal plane with a minimum of three traverses in each chordal plane, each chordal plane is in parallel with the conduit axis, wherein two nodes are each shared by two paths and a total number of nodes can be reduced from six to four or from seven to five.
 15. The ultrasonic flow meter system of claim 7, wherein the multiple transducer pairs located in the chordal measurement plane are positioned to form acoustic transmission paths, wherein three nodes are each shared by two paths and a total number of nodes can be reduced from seven to four.
 16. The ultrasonic flow meter system of claim 7, wherein the multiple transducer pairs located in the chordal measurement plane are positioned to form acoustic transmission paths that traverse at least once from one side, wherein two nodes are each shared by two paths and a third node is shared by three paths and a total number of nodes can be reduced from seven to three.
 17. The ultrasonic flow meter system of claim 7, wherein the multiple transducer pairs located in the chordal measurement plane are positioned to form acoustic transmission paths, wherein the acoustic transmission paths in each chordal plane overlap.
 18. A method for measuring fluid flow in a conduit with a flow meter, the flow meter comprising multiple transducer pairs positioned with respect to conduit acoustic transmission paths, the method comprising: providing an axial velocity measurement; providing a flow per unit time in the conduit using the axial velocity; providing an uncertainty measurement per unit time using the axial velocity measurement for each chordal plane; and providing an uncertainty quantity using the uncertainty measurement per unit time; and providing a total uncertainty quantity for a time period.
 19. The method of claim 18, further comprising: determining fluid flow in the conduit from the axial velocity measurement.
 20. The method of claim 18, comparing the total uncertainty quantity or the uncertainty quantity to a threshold to determine a fault.
 21. A flow meter system for measuring fluid flow in a conduit, the flow meter system comprising: a sensor configured to provide measurement data; a processor configured to determine: flow in the conduit using the measurement data at least one uncertainty value in quantity units per unit time using the measurement data, at least one uncertainty quantity using the uncertainty value per unit time, wherein the uncertainty quantity is totaled over a time period.
 22. The flow meter of claim 21, wherein two composite velocities are calculated using the axial velocity values from multiple chordal planes sensed by the sensor, with each of the two composite velocities being calculated using different chordal integration schemes, wherein the difference between the first and second composite velocities is used in the determination of the uncertainty value.
 23. The flow meter of claim 21, wherein the sensor comprises at least one of an: ultrasonic, Coriolis, electromagnetic, differential pressure, thermal, vortex shedding, cross-correlation, capacitance, microwave, temperature, pressure, or density sensor.
 24. The flow meter of claim 21, wherein the sensor use a reflected ultrasonic path to determine of an area uncertainty value, wherein the area uncertainty value is combined with a velocity result to yield an area related uncertainty in units of volume per time, wherein the area uncertainty value is totalised in units of volume. 